Highest Common Factor of 499, 821, 12 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 499, 821, 12 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 499, 821, 12 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 499, 821, 12 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 499, 821, 12 is 1.

HCF(499, 821, 12) = 1

HCF of 499, 821, 12 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 499, 821, 12 is 1.

Highest Common Factor of 499,821,12 using Euclid's algorithm

Highest Common Factor of 499,821,12 is 1

Step 1: Since 821 > 499, we apply the division lemma to 821 and 499, to get

821 = 499 x 1 + 322

Step 2: Since the reminder 499 ≠ 0, we apply division lemma to 322 and 499, to get

499 = 322 x 1 + 177

Step 3: We consider the new divisor 322 and the new remainder 177, and apply the division lemma to get

322 = 177 x 1 + 145

We consider the new divisor 177 and the new remainder 145,and apply the division lemma to get

177 = 145 x 1 + 32

We consider the new divisor 145 and the new remainder 32,and apply the division lemma to get

145 = 32 x 4 + 17

We consider the new divisor 32 and the new remainder 17,and apply the division lemma to get

32 = 17 x 1 + 15

We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get

17 = 15 x 1 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 499 and 821 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(32,17) = HCF(145,32) = HCF(177,145) = HCF(322,177) = HCF(499,322) = HCF(821,499) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 12 > 1, we apply the division lemma to 12 and 1, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12 is 1

Notice that 1 = HCF(12,1) .

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Frequently Asked Questions on HCF of 499, 821, 12 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 499, 821, 12?

Answer: HCF of 499, 821, 12 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 499, 821, 12 using Euclid's Algorithm?

Answer: For arbitrary numbers 499, 821, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.